A Tight Lower Bound for Planar Steiner Orientation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10403064" target="_blank" >RIV/00216208:11320/19:10403064 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/19:00338417
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cR7ytSXKfQ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cR7ytSXKfQ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00453-019-00580-x" target="_blank" >10.1007/s00453-019-00580-x</a>

Result language
angličtina
Original language name
A Tight Lower Bound for Planar Steiner Orientation
Original language description
In the Steiner Orientation problem, the input is a mixed graph G (it has both directed and undirected edges) and a set of k terminal pairs T. The question is whether we can orient the undirected edges in a way such that there is a directed s-t path for each terminal pair (s,t)T. Arkin and Hassin [DAM'02] showed that the Steiner Orientation problem is NP-complete. They also gave a polynomial time algorithm for the special case when k=2. From the viewpoint of exact algorithms, Cygan et al.[ESA'12, SIDMA'13] designed an XP algorithm running in n^O(k) time for all k>=1. Pilipczuk and Wahlstrom [SODA'16, TOCT'18] showed that the Steiner Orientation problem is W[1]-hard parameterized by k. As a byproduct of their reduction, they were able to show that under the Exponential Time Hypothesis (ETH) of Impagliazzo, Paturi and Zane [JCSS'01] the Steiner Orientation problem does not admit an f(k)*n^o(k/logk) algorithm for any computable function f. In this paper, we give a short and easy proof that the n^O(k) algorithm of Cygan etal. is asymptotically optimal, even if the input graph is planar. Formally, we show that the Planar Steiner Orientation problem is W[1]-hard parameterized by the number k of terminal pairs, and, under ETH, cannot be solved in f(k)n^o(k) time for any computable function f.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)